This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed.
Keywords: belief binarization; binary belief; credence; impossibility theorem; logic vs. rational choice theory; lottery paradox; subjective probability; yes/no belief vs. graded belief.
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